During a 60-minute period, a traffic engineer counted 54 trucks and cars that crossed a bridge. The ratio of trucks to cars that travel across the bridge is usually 2:7. The equation LaTeX: \frac{2}{7}=\frac{t}{54-t}2 7 = t 54 − t can be used to predict the number of trucks, t, the engineer should have counted. How many trucks should the engineer have counted?

Answer:

54 cans

HOPE THIS HELPS

-Todo <3

Step-by-step explanation:

4*12=48

48+6=54

The frequency of all the numbers are not similar as per the first table. Therefore, Suki's prediction is not correct

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The frequency of all the numbers are not similar as per the first table. In the first table 5 appears 5 times which is highest and 3 appear only once but in the second table,5 appear 48 times which is least and 3 appear 83 times which is not the least.

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ1

Answer:

B. -26

Here's a tip for next time:

First, enter the function into Desmos graphic calculator. Then, substitute x, -3 in this case, into the function to find the answer. The function in the calculator should look like this:

f(x) = -3^3 +1

Next, a line will appear and the point will give you your answer.

Desmos has helped me a lot, so hopefully it can be helpful for you too!

Answer:

1.4 cubic meters

Step-by-step explanation:

The jailer is correct in pointing out that if Prisoner A knew which of his fellow prisoners would be set free, his own probability of being executed would rise from 1/3 to 1/2. Therefore, the jailer's refusal to answer Prisoner A's question is justified based on probability calculations.

Scenario 1: Prisoner A is chosen for execution (1/3 probability)

In this case, if the jailer tells Prisoner A privately which of his fellow prisoners will be set free, it doesn't change the fact that Prisoner A is the one who will be executed. The information about the other prisoners' fate does not affect Prisoner A's own probability of being executed.

Scenario 2: Prisoner B is chosen for execution (1/3 probability)

In this scenario, if the jailer tells Prisoner A privately that Prisoner C will be set free, then Prisoner A's probability of being executed rises from 1/3 to 1/2. Knowing that one of the other two prisoners will be freed makes Prisoner A realize that if it's not B who is executed, then it must be him. So in this scenario, Prisoner A's probability of being executed does increase to 1/2.

Scenario 3: Prisoner C is chosen for execution (1/3 probability)

Similarly, if the jailer tells Prisoner A privately that Prisoner B will be set free, then Prisoner A's probability of being executed also rises from 1/3 to 1/2. Again, the knowledge that one of the other two prisoners will be freed indicates to Prisoner A that if it's not C who is executed, then it must be him.

From the above analysis, we can see that in two out of the three scenarios, Prisoner A's probability of being executed does indeed increase to 1/2 if he knows which fellow prisoner will be freed. Therefore, the jailer's reasoning is valid in denying Prisoner A's request for private information.

In summary, the jailer is correct in pointing out that if Prisoner A knew which of his fellow prisoners would be set free, his own probability of being executed would rise from 1/3 to 1/2. Therefore, the jailer's refusal to answer Prisoner A's question is justified based on probability calculations.

for such more question on probability

https://brainly.com/question/13604758

#SPJ11

The scale factor of the two rectangles show a common ratio of 4/5

A scale factor in geometry is a ratio that indicates how much a figure has been extended or shrunk.

When two figures are comparable, the scale factor is the ratio of any matching lengths in the two figures.

A scale factor of higher than 1 indicates expansion, whereas a scale factor of less than 1 indicates decrease. The figure is the same size as the original when the scale factor is 1.

The dimensions of comparable figures can be calculated using scale factors. For instance, we can use the scale factor to determine the length of the corresponding side of the smaller rectangle if we know the scale factor between two identical rectangles and the length of one of its sides of the larger rectangle.

In the given figure;

12/15 = 36/45

Let's find the ratio here;

4/5 =4/5

The scale factor is 4/5

Learn more on scale factor here;

https://brainly.com/question/10891847

#SPJ1

Answer:

your answer is 3

Step-by-step explanation:

let me know if I'm correct!

Answer:

\(x^{2} < 1\)

Step-by-step explanation:

The number of arrangements is 75600

To find the total number of different 10-letter arrangements that can be formed using the letters in the word INFINITIVE,

We can use the formula for permutations of a set of distinct objects.

First, we count the number of each distinct letter in the word INFINITIVE:

Using this information, we can calculate the total number of arrangements:

Total arrangements = 10! / (4! * 2! * 1! * 1! * 1! * 1!)

Evaluate

Total arrangements = 75600

Read more about combination at

https://brainly.com/question/11732255

#SPJ1

Answer:

Imperfect substitutes

explanation:

The choices above are not perfect substitutes, meaning they can not be perfectly or directly replace the other. Imperfect substitutes are close substitutes but not perfect substitutes. Unlike perfect substitutes, imperfect substitutes satisfies same utility but has different characteristics and therefore not entirely substitutable. For example, while one may want to have the 40 marks too, he'd rather have 60 marks even if the criteria for a 60 mark score was increasingly hard.

Answer:

========================

We have a diagram and need to find the number of routes without repeat paths:

We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.

This gives us the number of routes:

Total number is:

The matching answer choice is B

---------------------------------------------------------------------------

From the given we can observe that:

ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.

From similarity we get same ratio of corresponding sides:

We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:

As per ratio of corresponding sides:

As per segment addition:

From the two equations above we get:

Now, the required area is:

This is matching the answer choice D

Answer:

9)  B. 8

10)   D. 4.5

Step-by-step explanation:

Question 9

For ease of visualization, label the different legs of the journey on the diagram (see attachment).

The journey needs to start and end at point A, go through points B and C (in any order), and not travel any road twice.

The different routes are:

Therefore, there are 8 different routes.

Question 10

Triangles EDC and EAB are similar since they have congruent angles:

Therefore, their corresponding sides are in proportion.

⇒ CD : BA = ED : EA

⇒ 9 : 3 = ED : EA

⇒ 3 : 1 = ED : EA

Since we know that AD = 4:

⇒ ED = 3

⇒ EA = 1

Area of a triangle

\(\sf Area = \dfrac{1}{2} \times base \times height\)

To find the area of triangle AEC, subtract the area of triangle EDC from the area of triangle ADC.

\(\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}\)

Learn more about similar triangles here:

https://brainly.com/question/21427237

When r = 2, the value of M is 20 when m is directly proportional to r³.

If we know that M is directly proportional to r³, we can write this relationship as:

M = k * r³,

where k is the constant of proportionality. To find the value of k, we can use the given information when r = 4 and M = 160:

160 = k * 4³.

Simplifying the equation:

160 = k * 64,

k = 160 / 64,

k = 2.5.

Now that we have determined the value of k, we can use it to find the value of M when r = 2. We plug r = 2 and k = 2.5 into the equation:

M = 2.5 * 2³,

M = 2.5 * 8,

M = 20.

Therefore, when r = 2, the value of M is 20.

The direct proportionality between M and r³ means that as r increases, M will increase at a faster rate, specifically cubed. In this case, when r doubles from 2 to 4, M increases by a factor of 8 (2³ = 8).

For more such questions on proportional visit:

https://brainly.com/question/1496357

#SPJ8

There are n different values that the remainder r can take on when \(n^2\) is divided by n 4.

We can use the Remainder Theorem to solve this problem. The Remainder Theorem states that when a polynomial f(x) is divided by (x-a), the remainder is f(a).

Using this theorem, we can see that \(n^2\) divided by n 4 leaves a remainder of \(n^2 - kn 4\), where k is some integer. We want to find how many different values r can take on, which is the same as finding how many different values \($n^2 - kn 4$\) can take on.

Let's rewrite \(n^2 - kn 4 as n(n - k 4)\). This expression tells us that n and n - k 4 have the same remainder when divided by n 4. Therefore, n - k 4 can only take on n different values, namely \(0, n, 2n, \ldots, (n-1)n.\)

For each of these n values, we can find a corresponding value of k that satisfies\($n^2 - kn 4 \equiv r \pmod{n 4}$\), namely \(k = (n^2 - r)/(n 4).\) Therefore, there are exactly n different values that r can take on.

for such more question on remainder

https://brainly.com/question/11536181

#SPJ11

Answer:

hifgreeg33ctvtvunu

Step-by-step explanation:

highhb tug 5h6g6g5g5g

Answer:

51/20

Explanation:

14/5-1/4=

14*4/5*4-1*5/4*5=

56/20-5/20=

56-5/20=

51/20

a) To find the values of T₁, T₂, and T₄ using the composite trapezoidal rule, we need to divide the interval [1, 2] into n subintervals and calculate the corresponding approximations.

b) To approximate the integral ∫[1 to 2] f²(x) dx using the values of T₁, T₂, and T obtained in part a), we can use Richardson's extrapolation formula

For T₁, we have n = 1 (one subinterval):

Δx = (2 - 1) / 1 = 1

T₁ = Δx/2 * [f(1) + f(2)]

= (1/2) * [f(1) + f(2)]

For T₂, we have n = 2 (two subintervals):

Δx = (2 - 1) / 2 = 1/2

T₂ = Δx/2 * [f(1) + 2f(3/2) + f(2)]

For T₄, we have n = 4 (four subintervals):

Δx = (2 - 1) / 4 = 1/4

T₄ = Δx/2 * [f(1) + 2f(5/4) + 2f(3/2) + 2f(7/4) + f(2)]

b) To approximate the integral ∫[1 to 2] f²(x) dx using the values of T₁, T₂, and T obtained in part a), we can use Richardson's extrapolation formula. This formula allows us to improve the accuracy of the approximation.

Richardson's extrapolation formula:

I ≈ (4T₂ - T₁) / 3

Using this formula, we can plug in the values of T₁ and T₂ obtained in part a) to get a more accurate approximation of the integral ∫[1 to 2] f²(x) dx.

I ≈ (4T₂ - T₁) / 3

Please note that without the specific function f(x) provided, we cannot provide the exact numerical values for T₁, T₂, and the final approximation of the integral. The above formulas represent the general process for finding these values using the composite trapezoidal rule and Richardson's extrapolation.

Learn more about subintervals here

https://brainly.com/question/10207724

#SPJ11

The probability that they both own a dog is,

⇒ 0.2209

We have to given that;

Suppose that 47% of people own dogs.

And, you pick two people at random.

Now,

P (First person owns dogs) = 47/100 = 0.47

⇒ 47% of those 47% of the time the second person you pick will own a dog.

P (Second person owns dogs) = 47/100 = 0.47

Thus, The probability that they both own a dog is,

⇒ P (both owns dogs) = (0.47) × (0.47) = 0.2209

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

Answer:

Kitten is 15 seconds and dog is 10 seconds

In work and time the time taken is inversely proportional to the work done. Work and time is a concept to solve the problems of work related question in a given time.The kitten eats a sausage in 15 seconds  and puppy eats a sausage in 10 seconds.

In work and time the time taken is inversely proportional to the work done. Work and time is a concept to solve the problems of work related question in a given time

Puppy and kitten eats one sausage combined in 6 sec.

A puppy eats a sausage 5 seconds faster than a kitten eats an identical sausage.

Let puppy eats a sausage in \(x\) seconds and kitten eats a sausage in \(y\) seconds.

As Puppy and kitten eats one sausage combined in 6 sec.Thus,

\(\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{6}\)

Let above equation is equation one.

A puppy eats a sausage 5 seconds faster than a kitten eats an identical sausage. Thus

\(\dfrac{1}{x} -\dfrac{1}{y}=\dfrac{1}{5}\)

Put this value of \(x\) in the  the equation one to get the value of y. Therefore,

\(\dfrac{1}{6} -\dfrac{1}{y}-\dfrac{1}{y}=\dfrac{1}{5}\)

\(-\dfrac{1}{2y}=\dfrac{1}{5}-\dfrac{1}{6}\)

\(-\dfrac{1}{2y}=-\dfrac{1}{30}\)

\(y=15\)

Thus the kitten eats a sausage in 15 seconds.

Put the value of y in equation one. thus,

\(\dfrac{1}{x} +\dfrac{1}{15} =\dfrac{1}{6}\)

\(\dfrac{1}{x} =\dfrac{1}{6}-\dfrac{1}{15}\)

\(\dfrac{1}{x} =\dfrac{9}{90}\)

\(x=10\)

Thus the puppy eats a sausage in 10 seconds.

Hence the kitten eats a sausage in 15 seconds  and  puppy eats a sausage in 10 seconds.

Learn more about the work and time here,

https://brainly.com/question/8536605

Sampling Error is defined as; the discrepancy between a sample estimate of a population parameter and the real population parameter.

A sampling error is defined as a deviation that occurs in the sampled value when compared to the true population value. Now, sampling errors usually occur due to the fact that the sample is not representative of the population or is biased in some way.

The sampling error formula is used to estimate the overall sampling error in any given statistical analysis. The way we calculate the sampling error is by dividing the standard deviation of the population by the square root of the size of the sample, and thereafter multiplying the result with the Z-score value, which is largely based on the confidence interval.

Looking at the options, from the definitions above, it is clear that the sampling error is defined by option C

Read more about Sampling Error at; https://brainly.com/question/28008941

#SPJ1

The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

To learn more about square root, click here:

brainly.com/question/29286039

#SPJ4

The XYZ corporation will receive $1500000 for all the shares sold.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given: Cost of 1 share = $15

To find: Money received on selling 100000 shares.

Finding:

By unitary method,

Money received on selling 1 share = $15

Money received on selling 100000 shares = 15(100000) = $1500000

Hence, The XYZ corporation will receive $1500000 for all the shares sold.

To learn more about unitary method, refer to the link: https://brainly.com/question/24587372

#SPJ4

Part A: The two transformations that could be performed on Figure A to show the figures are congruent are: A reflection across the x-axis, A translation directly to the right.

Part A: The two transformations that could be performed on Figure A to show the figures are congruent are:

1. A reflection across the x-axis.

2. A translation directly to the right.

Part B: The true statement about Figure A, Figure A', and Figure A'' is:

Only Figure A is congruent to Figure A'.

Learn more about transformations at https://brainly.com/question/4289712

#SPJ1

Answer:

El área de un círculo se puede calcular utilizando la fórmula A = πr², donde r es el radio del círculo. Como el diámetro del círculo es de 20 cm, el radio será la mitad de ese valor, es decir, 10 cm. Por lo tanto, el área del círculo sería:

A = πr²

A = π(10 cm)²

A = π(100 cm²)

Aproximadamente, el área es de 314,16 cm².

The dimensions of the box are 12 inches by 2 inches by 4 inches.

Let's use variables to represent the dimensions of the box:

Let h be the height of the box (in inches).

Then, the length of the box is 8 inches more than the height, so it is h + 8.

The width of the box is 2 inches less than the height, so it is h - 2.

The volume of the box is given as 96 cubic inches, so we can set up an equation:

Volume = Length × Width × Height

96 = (h + 8) × (h - 2) × h

h = 4

Height: h = 4 inches

Length: h + 8 = 12 inches

Width: h - 2 = 2 inches

Therefore, the dimensions of the box are 12 inches by 2 inches by 4 inches.

Learn more about volume here:

https://brainly.com/question/23952628

#SPj1

Answer:

A

Total before tax: $118

Total after tax: $102.66

Step-by-step explanation:

For A, we add the cost of the shirt and jeans to get the total before tax.

$39.20 + $79.80 = $118.00

For the total, after 13% we see how much 1% is.

1% of $118 is $1.18

$1.18 * 13 = $15.34.

$118 - $15.34 = $102.66

Hope this helped! Have a nice day :)

we can see that the small box offers the best value for money with a cost of £0.34 per coffee pod. Therefore, the answer isThe small box gives the best value for money.

To determine the best value for money among the three sizes of coffee pod boxes, we need to calculate the cost per coffee pod for each size of the box.

For a small box with 12 coffee pods costing £4.08, the cost per coffee pod can be calculated as:

Cost per coffee pod = £4.08 ÷ 12 = £0.34

For a medium box with 20 coffee pods costing £7.80, the cost per coffee pod can be calculated as:

Cost per coffee pod = £7.80 ÷ 20 = £0.39

For a large box with 35 coffee pods costing £12.95, the cost per coffee pod can be calculated as:

Cost per coffee pod = £12.95 ÷ 35 = £0.37

Comparing the cost per coffee pod for each box size, we can see that the small box offers the best value for money with a cost of £0.34 per coffee pod. Therefore, the answer is:

The small box gives the best value for money.

To know more about Cost visit:

brainly.com/question/19075809

#SPJ1

Answer:

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... This form of a line's equation is called the slope-intercept form, because can be interpreted as the y-intercept of the line, that is, the y-coordinate where the line intersects the y-axis.

Step-by-step explanation:

pls i rly need brainly to level up ty

Answer:

Step-by-step explanation:

The pairing is not a function, as the input 2 is mapped to two different outputs.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

From the table, the mappings are given as follows:

More can be learned about relations and functions at https://brainly.com/question/12463448

#SPJ1

The probability directly from the cumulative distributive function:

P(X = 2) = 0.17 , P(X > 3) =  0.31 , P(2 ≤ X ≤ 5) = 0.76, P(2 < X < 5)  = 0.42 ,

These calculations are essential in many areas of probability theory and statistics, including hypothesis testing, confidence intervals, and estimation.

(a) To find P(X = 2), we subtract the probability of the previous value from the probability of X being less than or equal to 2:

P(X = 2) = F(2) - F(1) = 0.33 - 0.16 = 0.17.

(b) To find P(X > 3), we subtract the probability of X being less than or equal to 3 from 1:

P(X > 3) = 1 - F(3) = 1 - 0.69 = 0.31.

(c) To find P(2 ≤ X ≤ 5), we subtract the probability of X being less than 2 from the probability of X being less than or equal to 5:

P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.92 - 0.16 = 0.76.

(d) To find P(2 < X < 5), we subtract the probability of X being less than or equal to 2 from the probability of X being less than or equal to 5, and then subtract the probability of X being equal to 2:

P(2 < X < 5) = F(5) - F(2) - P(X = 2) = 0.92 - 0.33 - 0.17 = 0.42.

In summary, to calculate probabilities from a given cdf, we use the formula P(X = x) = F(x) - F(x-1) for discrete random variables, and P(a < X ≤ b) = F(b) - F(a) for continuous random variables. We can also use complement probabilities to find the probability of events such as P(X > a) or P(a < X < b). These calculations are essential in many areas of probability theory and statistics, including hypothesis testing, confidence intervals, and estimation.

Learn more about Probability:

https://brainly.com/question/11234923

#SPJ4